The Convergence Rate of High-Dimensional Sample Quantiles for φ-Mixing Observation Sequences

Abstract

In this paper, we obtain the convergence rate for the high-dimensional sample quantiles with the φ-mixing dependent sequence. The resulting convergence rate is shown to be faster than that obtained by the Hoeffding-type inequalities. Moreover, the convergence rate of the high-dimensional sample quantiles for the observation sequence taking discrete values is also provided.